I'm afraid we don't have any pages that specifically address acronyms, but the Cambridge Dictionary has a good page on Abbreviations, initials and acronyms that might be helpful to you. Or if you have a specific question, please feel free to ask us.

I expect you could find examples of this kind of sentence in published texts, but I personally would avoid it in favour of something like 'People have disagreed on this matter and still do' because 'have' is followed by the past participle 'disagreed' and 'do' is followed by the bare infinitive 'disagree'.

Leaving out words that can be understood from context is called ellipsis -- if you follow the link, you can see a good explanation of it there.